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19 pages, 983 KiB

Open AccessArticle

An Efficient Closed-Form Formula for Evaluating r-Flip Moves in Quadratic Unconstrained Binary Optimization

by Bahram Alidaee, Haibo Wang and Lutfu S. Sua

Algorithms 2023, 16(12), 557; https://doi.org/10.3390/a16120557 - 05 Dec 2023

Viewed by 1295

Quadratic unconstrained binary optimization (QUBO) is a classic NP-hard problem with an enormous number of applications. Local search strategy (LSS) is one of the most fundamental algorithmic concepts and has been successfully applied to a wide range of hard combinatorial optimization problems. One [...] Read more.

Quadratic unconstrained binary optimization (QUBO) is a classic NP-hard problem with an enormous number of applications. Local search strategy (LSS) is one of the most fundamental algorithmic concepts and has been successfully applied to a wide range of hard combinatorial optimization problems. One LSS that has gained the attention of researchers is the r-flip (also known as r-Opt) strategy. Given a binary solution with n variables, the r-flip strategy “flips” r binary variables to obtain a new solution if the changes improve the objective function. The main purpose of this paper is to develop several results for the implementation of r-flip moves in QUBO, including a necessary and sufficient condition that when a 1-flip search reaches local optimality, the number of candidates for implementation of the r-flip moves can be reduced significantly. The results of the substantial computational experiments are reported to compare an r-flip strategy-embedded algorithm and a multiple start tabu search algorithm on a set of benchmark instances and three very-large-scale QUBO instances. The r-flip strategy implemented within the algorithm makes the algorithm very efficient, leading to very high-quality solutions within a short CPU time. Full article

(This article belongs to the Special Issue Metaheuristics)

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25 pages, 1780 KiB

Open AccessArticle

A Hybrid Optimization Framework with Dynamic Transition Scheme for Large-Scale Portfolio Management

by Zhenglong Li and Vincent Tam

Algorithms 2022, 15(11), 404; https://doi.org/10.3390/a15110404 - 31 Oct 2022

Viewed by 1339

Abstract

Meta-heuristic algorithms have successfully solved many real-world problems in recent years. Inspired by different natural phenomena, the algorithms with special search mechanisms can be good at tackling certain problems. However, they may fail to solve other problems. Among the various approaches, hybridizing meta-heuristic [...] Read more.

Meta-heuristic algorithms have successfully solved many real-world problems in recent years. Inspired by different natural phenomena, the algorithms with special search mechanisms can be good at tackling certain problems. However, they may fail to solve other problems. Among the various approaches, hybridizing meta-heuristic algorithms may possibly help to enrich their search behaviors while promoting the search adaptability. Accordingly, an efficient hybrid population-based optimization framework, namely the HYPO, is proposed in this study in which two meta-heuristic algorithms with different search ideas are connected by a dynamic contribution-based state transition scheme. Specifically, the dynamic transition scheme determines the directions of information transitions after considering the current contribution and system state at each iteration so that useful information can be shared and learnt between the concerned meta-heuristic algorithms throughout the search process. To carefully examine the effectiveness of the dynamic transition scheme, the proposed HYPO framework is compared against various well-known meta-heuristic algorithms on a set of large-scale benchmark functions and portfolio management problems of different scales in which the HYPO attains outstanding performances on the problems with complex features. Last but not least, the hybrid framework sheds lights on many possible directions for further improvements and investigations. Full article

(This article belongs to the Special Issue Metaheuristics)

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14 pages, 430 KiB

Open AccessArticle

Computational Performance Evaluation of Column Generation and Generate-and-Solve Techniques for the One-Dimensional Cutting Stock Problem

by José Victor Sá Santos and Napoleão Nepomuceno

Algorithms 2022, 15(11), 394; https://doi.org/10.3390/a15110394 - 25 Oct 2022

Cited by 1 | Viewed by 1171

Abstract

The Cutting Stock Problem (CSP) is an optimisation problem that roughly consists of cutting large objects in order to produce small items. The computational effort for solving this problem is largely affected by the number of cutting patterns. In this article, in order [...] Read more.

The Cutting Stock Problem (CSP) is an optimisation problem that roughly consists of cutting large objects in order to produce small items. The computational effort for solving this problem is largely affected by the number of cutting patterns. In this article, in order to cope with large instances of the One-Dimensional Cutting Stock Problem (1D-CSP), we resort to a pattern generating procedure and propose a strategy to restrict the number of patterns generated. Integer Linear Programming (ILP) models, an implementation of the Column Generation (CG) technique, and an application of the Generate-and-Solve (G&S) framework were used to obtain solutions for benchmark instances from the literature. The exact method was capable of solving small and medium sized instances of the problem. For large sized instances, the exact method was not applicable, while the effectiveness of the other methods depended on the characteristics of the instances. In general, the G&S method presented successful results, obtaining quasi-optimal solutions for the majority of the instances, by employing the strategy of artificially reducing the number of cutting patterns and by exploiting them in a heuristic framework. Full article

(This article belongs to the Special Issue Metaheuristics)

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24 pages, 4148 KiB

Open AccessArticle

Micro-Scale Spherical and Cylindrical Surface Modeling via Metaheuristic Algorithms and Micro Laser Line Projection

by J. Apolinar Muñoz Rodríguez

Algorithms 2022, 15(5), 145; https://doi.org/10.3390/a15050145 - 24 Apr 2022

Cited by 2 | Viewed by 1943

Abstract

With the increasing micro-scale manufacturing industry, the micro-scale spherical and cylindrical surface modeling has become an important factor in the manufacturing process. Thus, the micro-scale manufacturing processes require efficient micro-scale spherical and cylindrical models to achieve accurate assembly. Therefore, it is necessary to [...] Read more.

With the increasing micro-scale manufacturing industry, the micro-scale spherical and cylindrical surface modeling has become an important factor in the manufacturing process. Thus, the micro-scale manufacturing processes require efficient micro-scale spherical and cylindrical models to achieve accurate assembly. Therefore, it is necessary to implement models to represent micro-scale spherical and cylindrical surfaces. This study addresses metaheuristic algorithms based on micro laser line projection to perform micro-scale spherical and cylindrical surface modeling. In this technique, the micro-scale surface is recovered by an optical microscope system, which computes the surface coordinates via micro laser line projection. From the surface coordinates, a genetic algorithm determines the parameters of the mathematical models to represent the spherical and cylindrical surfaces. The genetic algorithm performs exploration and exploitation in the search space to optimize the models’ mathematical parameters. The search space is constructed via surface data to provide the optimal parameters, which determine the spherical and cylindrical surface models. The proposed technique improves the fitting accuracy of the micro-scale spherical and cylindrical surface modeling performed via optical microscope systems. This contribution is elucidated by a discussion about the model fitting between the genetic algorithms based on micro laser line projection and the optical microscope systems. Full article

(This article belongs to the Special Issue Metaheuristics)

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22 pages, 1773 KiB

Open AccessArticle

On Parameter Identification for Reaction-Dominated Pore-Scale Reactive Transport Using Modified Bee Colony Algorithm

by Vasiliy V. Grigoriev, Oleg Iliev and Petr N. Vabishchevich

Algorithms 2022, 15(1), 15; https://doi.org/10.3390/a15010015 - 30 Dec 2021

Cited by 3 | Viewed by 2412

Abstract

Parameter identification is an important research topic with a variety of applications in industrial and environmental problems. Usually, a functional has to be minimized in conjunction with parameter identification; thus, there is a certain similarity between the parameter identification and optimization. A number [...] Read more.

Parameter identification is an important research topic with a variety of applications in industrial and environmental problems. Usually, a functional has to be minimized in conjunction with parameter identification; thus, there is a certain similarity between the parameter identification and optimization. A number of rigorous and efficient algorithms for optimization problems were developed in recent decades for the case of a convex functional. In the case of a non-convex functional, the metaheuristic algorithms dominate. This paper discusses an optimization method called modified bee colony algorithm (MBC), which is a modification of the standard bees algorithm (SBA). The SBA is inspired by a particular intelligent behavior of honeybee swarms. The algorithm is adapted for the parameter identification of reaction-dominated pore-scale transport when a non-convex functional has to be minimized. The algorithm is first checked by solving a few benchmark problems, namely finding the minima for Shekel, Rosenbrock, Himmelblau and Rastrigin functions. A statistical analysis was carried out to compare the performance of MBC with the SBA and the artificial bee colony (ABC) algorithm. Next, MBC is applied to identify the three parameters in the Langmuir isotherm, which is used to describe the considered reaction. Here, 2D periodic porous media were considered. The simulation results show that the MBC algorithm can be successfully used for identifying admissible sets for the reaction parameters in reaction-dominated transport characterized by low Pecklet and high Damkholer numbers. Finite element approximation in space and implicit time discretization are exploited to solve the direct problem. Full article

(This article belongs to the Special Issue Metaheuristics)

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31 pages, 4725 KiB

Open AccessArticle

The Stock Index Prediction Based on SVR Model with Bat Optimization Algorithm

by Jianguo Zheng, Yilin Wang, Shihan Li and Hancong Chen

Algorithms 2021, 14(10), 299; https://doi.org/10.3390/a14100299 - 15 Oct 2021

Cited by 14 | Viewed by 2597

Abstract

Accurate stock market prediction models can provide investors with convenient tools to make better data-based decisions and judgments. Moreover, retail investors and institutional investors could reduce their investment risk by selecting the optimal stock index with the help of these models. Predicting stock [...] Read more.

Accurate stock market prediction models can provide investors with convenient tools to make better data-based decisions and judgments. Moreover, retail investors and institutional investors could reduce their investment risk by selecting the optimal stock index with the help of these models. Predicting stock index price is one of the most effective tools for risk management and portfolio diversification. The continuous improvement of the accuracy of stock index price forecasts can promote the improvement and maturity of China’s capital market supervision and investment. It is also an important guarantee for China to further accelerate structural reforms and manufacturing transformation and upgrading. In response to this problem, this paper introduces the bat algorithm to optimize the three free parameters of the SVR machine learning model, constructs the BA-SVR hybrid model, and forecasts the closing prices of 18 stock indexes in Chinese stock market. The total sample comes from 15 January 2016 (the 10th trading day in 2016) to 31 December 2020. We select the last 20, 60, and 250 days of whole sample data as test sets for short-term, mid-term, and long-term forecast, respectively. The empirical results show that the BA-SVR model outperforms the polynomial kernel SVR model and sigmoid kernel SVR model without optimized initial parameters. In the robustness test part, we use the stationary time series data after the first-order difference of six selected characteristics to re-predict. Compared with the random forest model and ANN model, the prediction performance of the BA-SVR model is still significant. This paper also provides a new perspective on the methods of stock index forecasting and the application of bat algorithms in the financial field. Full article

(This article belongs to the Special Issue Metaheuristics)

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13 pages, 363 KiB

Open AccessArticle

Ant Colony Optimization with Warm-Up

by Mattia Neroni

Algorithms 2021, 14(10), 295; https://doi.org/10.3390/a14100295 - 12 Oct 2021

Cited by 9 | Viewed by 2096

Abstract

The Ant Colony Optimization (ACO) is a probabilistic technique inspired by the behavior of ants for solving computational problems that may be reduced to finding the best path through a graph. Some species of ants deposit pheromone on the ground to mark some [...] Read more.

The Ant Colony Optimization (ACO) is a probabilistic technique inspired by the behavior of ants for solving computational problems that may be reduced to finding the best path through a graph. Some species of ants deposit pheromone on the ground to mark some favorable paths that should be used by other members of the colony. Ant colony optimization implements a similar mechanism for solving optimization problems. In this paper a warm-up procedure for the ACO is proposed. During the warm-up, the pheromone matrix is initialized to provide an efficient new starting point for the algorithm, so that it can obtain the same (or better) results with fewer iterations. The warm-up is based exclusively on the graph, which, in most applications, is given and does not need to be recalculated every time before executing the algorithm. In this way, it can be made only once, and it speeds up the algorithm every time it is used from then on. The proposed solution is validated on a set of traveling salesman problem instances, and in the simulation of a real industrial application for the routing of pickers in a manual warehouse. During the validation, it is compared with other ACO adopting a pheromone initialization technique, and the results show that, in most cases, the adoption of the proposed warm-up allows the ACO to obtain the same or better results with fewer iterations. Full article

(This article belongs to the Special Issue Metaheuristics)

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19 pages, 460 KiB

Open AccessArticle

The Power of Human–Algorithm Collaboration in Solving Combinatorial Optimization Problems

by Tapani Toivonen and Markku Tukiainen

Algorithms 2021, 14(9), 253; https://doi.org/10.3390/a14090253 - 24 Aug 2021

Cited by 1 | Viewed by 2397

Abstract

Many combinatorial optimization problems are often considered intractable to solve exactly or by approximation. An example of such a problem is maximum clique, which—under standard assumptions in complexity theory—cannot be solved in sub-exponential time or be approximated within the polynomial factor efficiently. [...] Read more.

Many combinatorial optimization problems are often considered intractable to solve exactly or by approximation. An example of such a problem is maximum clique, which—under standard assumptions in complexity theory—cannot be solved in sub-exponential time or be approximated within the polynomial factor efficiently. However, we show that if a polynomial time algorithm can query informative Gaussian priors from an expert poly(n) times, then a class of combinatorial optimization problems can be solved efficiently up to a multiplicative factor ϵ, where ϵ is arbitrary constant. In this paper, we present proof of our claims and show numerical results to support them. Our methods can cast new light on how to approach optimization problems in domains where even the approximation of the problem is not feasible. Furthermore, the results can help researchers to understand the structures of these problems (or whether these problems have any structure at all!). While the proposed methods can be used to approximate combinatorial problems in NPO, we note that the scope of the problems solvable might well include problems that are provable intractable (problems in EXPTIME). Full article

(This article belongs to the Special Issue Metaheuristics)

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